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Abstract
Study objective: Using a conceptual rather than a mathematical approach, this article proposed a link between multilevel regression analysis (MLRA) and social epidemiological concepts. It has been previously explained that the concept of clustering of individual health status within neighbourhoods is useful for operationalising contextual phenomena in social epidemiology. It has been shown that MLRA permits investigating neighbourhood disparities in health without considering any particular neighbourhood characteristic but only information on the neighbourhood to which each person belongs. This article illustrates how to analyse cross level (neighbourhood–individual) interactions, how to investigate associations between neighbourhood characteristics and individual health, and how to use the concept of clustering when interpreting those associations and geographical differences in health.
Design and participants: A MLRA was performed using hypothetical data pertaining to systolic blood pressure (SBP) from 25 000 subjects living in the 39 neighbourhoods of an imaginary city. Associations between individual characteristics (age, body mass index (BMI), use of antihypertensive drug, income) or neighbourhood characteristic (neighbourhood income) and SBP were analysed.
Results: About 8% of the individual differences in SBP were located at the neighbourhood level. SBP disparities and clustering of individual SBP within neighbourhoods increased along individual BMI. Neighbourhood low income was associated with increased SBP over and above the effect of individual characteristics, and explained 22% of the neighbourhood differences in SBP among people of normal BMI. This neighbourhood income effect was more intense in overweight people.
Conclusions: Measures of variance are relevant to understanding geographical and individual disparities in health, and complement the information conveyed by measures of association between neighbourhood characteristics and health.
- MLRA, multilevel regression analysis
- SBP, systolic blood pressure
- BMI, body mass index
- AHD, antihypertensive drug
- MLRA, multilevel regression analysis
- VPC, variance partition coefficient
- PCV, proportional change in variance
- multilevel analysis
- social epidemiology
- health inequalities
- tutorial
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Footnotes
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↵* The “empty” MLRA model (model i) is a model without any independent variable. The outcome (for example, SBP) is only function of the area in which the people live, which is accounted for with an area level random intercept. See elsewhere12 for a more detailed explanation.
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↵† In the model with the random slope (model iii) we assume that the effect of BMI on SBP may be different from one neighbourhood to another. In that case, the slope of the association between BMI and SBP would vary from one neighbourhood to another and neighbourhood disparities become a function of individual BMI. See elsewhere13 for a more detailed explanation.
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↵‡ In the model with non-constant individual variance we assume that within each neighbourhood, individual SBP differences were larger among people who were overweight than among people of normal BMI. In statistical terms this phenomenon is called individual level heteroscedasticity, meaning that the individual level variance in SBP is not constant along BMI. Absence of heteroscedasticity is a condition for performing correct regression analysis. We can use MLRA to model non-constant individual level variance and obtain both relevant epidemiological information and correct regression estimates.
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↵§ “Fixed effects” and “random effects” are expressions that are often used in MLRA. Essentially, fixed effects are used to model averages and refer to the usual regression coefficients, whereas random effects are used to model differences (for example, neighbourhood variance).
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↵¶ The shrunken differences or shrunken residuals can be estimated using the raw residuals, the estimated variances, and the number of people in each neighbourhood. The fewer the number of people in a neighbourhood, or the higher the variability within neighbourhoods as compared with the variability between neighbourhoods, the more important the shrinkage and the more the value of the neighbourhood residual will be shrunken towards 0. See elsewhere12 for a more detailed explanation.
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↵** Note that BMI may be in the causal pathway between neighbourhood low income and individual SBP. Whether you should adjust or not for BMI in that case depends on whether BMI is conceptualised as a confounding factor or as mediating factor. If the social environment influences health by operating as contextual determinants of other individual characteristics, then controlling for many individual factors may result in over-adjusting the true effects of the context.
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Funding: this study was supported by grants from FAS (Swedish Council for Working Life and Social Research) for the projects “Development and application of multilevel analysis in pharmacoepidemiology and social medicine” (principal investigator Juan Merlo, no 2002-054) and “Socioeconomic disparities in cardiovascular diseases—a longitudinal multilevel analysis” (principal investigator Juan Merlo, no 2003-0580).
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Competing interests: none declared.